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The aim of this book is to give a systematic and self-contained presentation of the basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by It and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measures on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof.

Stochastic partial differential equations --- Stochastic partial differential equations. --- Stochastic processes --- Équations aux dérivées partielles stochastiques

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Stochastic processes --- Stochastic partial differential equations. --- Wave equation. --- Random fields. --- Équations aux dérivées partielles stochastiques --- Equation d'onde --- Champs aléatoires --- 51 <082.1> --- Mathematics--Series --- Équations aux dérivées partielles stochastiques. --- Équations d'onde. --- Champs aléatoires. --- Équations aux dérivées partielles stochastiques --- Champs aléatoires --- Random fields --- Stochastic partial differential equations --- Wave equation --- Differential equations, Partial --- Wave-motion, Theory of --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Fields, Random